Problem
GEO-B2-M07-P009 Point on a Median
#9
★★★☆☆ Level 3 of 5
In triangle \(ABC\), median \(AM\) passes through an interior point \(P\). Prove that \([PAB]=[PAC]\).
Line \(AP\) meets \(BC\) at midpoint \(M\).
By the formula, \(\frac{[PAB]}{[PAC]}=\frac{BM}{MC}\). Since \(M\) is the midpoint of \(BC\), \(BM=MC\). Therefore \([PAB]=[PAC]\).
The reverse side of the midpoint example.